I Do ferromagnetic materials do "spatial averaging"?

I have a classical E&M physics problem that I've been tearing my hair out over. It relates to how ferromagnetic materials boost the field strength of a non-uniform magnetic field. My takeaway from college physics class was that (assuming there's no saturation in the material) the field inside a magnetic material is boosted linearly by a multiplicative constant. So if the field vector at any point in free space p is B(p), if that point in space is enclosed within a magnetic material, the field vector will be αB(p), where α is the relative permeability of the material. But based on some measurements I did, this doesn't appear that my takeaway was correct. It appears instead that there's some sort of "spatial averaging" going on inside the magnetic material, leaving me totally confused. Please see attached for a detailed description of my problem, with images, etc.

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

I have a classical E&M physics problem that I've been tearing my hair out over. It relates to how ferromagnetic materials boost the field strength of a non-uniform magnetic field. My takeaway from college physics class was that (assuming there's no saturation in the material) the field inside a magnetic material is boosted linearly by a multiplicative constant. So if the field vector at any point in free space p is B(p), if that point in space is enclosed within a magnetic material, the field vector will be αB(p), where α is the relative permeability of the material. But based on some measurements I did, this doesn't appear that my takeaway was correct. It appears instead that there's some sort of "spatial averaging" going on inside the magnetic material, leaving me totally confused. Please see attached for a detailed description of my problem, with images, etc.

In your simulation you use an arbitrary increase by a factor of 10 for the induced field within the ferrite core. Have you tried looking up the relative permeability of ferrite (it is more like 640)? Your approach of linear amplification of the induced field within the ferrite does not deal with continuity of the fields and derivatives of the fields at the boundaries of the ferrite material. Any solution of Maxwells equations has to include the behaviour at the boundaries between materials. This will modify the induced field distribution inside the inner perimeter of the ferrite material, within the ferrite material and external to the outer perimeter of the ferrite. The finite length of your ferrite will introduce similar boundary conditions at the axial endpoints as well. What does your experimental measurement suggest is happening? What conclusion can you therefore draw about the your simple linear amplification model of the field within the ferrite?